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01/20/11

Photovoltaic Capacitance and Time Domain Measurements

I noticed that my PV test blog posts have been getting a lot of hits so I wanted to capture an area of PV test that I have not touched on yet and is out of the normal GPETE realm. That area is photovoltaic capacitance and time domain testing. This type of testing provides deep dive into the physics of PV cell for improving improving the cell's efficiency at the material fabrication level..
We are all familiar with I-V measurements made throughout the PV product design cycle. With I-V measurements we can calculate PV parameters like Isc, Voc, FF, Pmax, etc.Capacitance measurements and time domain measurements are required to completely characterize solar cells. Because traps in the bulk material directly affect carrier recombination at the interface and in the bulk, it is essential to characterize these traps so as to minimize their impact on solar cell performance. Capacitance measurements are the main method to evaluate traps in the bulk. Understanding trap behavior is also important when studying multi-junction PV cells and for controlling the PV cell band gap. To optimize PV cell performance it is also important to know the carrier diffusion length, because it is one of the key parameters impacting PV cell efficiency. Time domain measurement is the principal method used to measure carrier diffusion length. The following figure lists PV parameters that can be obtained from capacitance and time domain measurements.

In the next couple paragraphs I will briefly explain the parameters in capacitance and time domain measurements. I will warn you the math gets a little heavy so if you are just interested in a solution for making these measurements refer to the link at the end of the post.

CV measurements, which are the most common capacitance measurements, can be used to estimate the carrier density (Nc) using the following equation.

Here q is the electron charge, Ks is the semiconductor dielectric constant, ε0 is the permittivity of free space, A is the surface area of a PV cell and Vbi is the built-in potential. A 1/C2 - V plot is called a Mott-Schottky plot, and the Nc distribution over the depletion width (W) is obtained from the slope of Mott-Schottky plot as shown below (click to enlarge).

An AC voltage capacitance measurement (CVac) provides the information about the defect density (Nd). This technique is known as drive-level capacitance profiling (DLCP), and it is used to determine deep defect densities by studying the non-linear response of the capacitor

as a function of the peak-to-peak voltage dV (=Vpp) of the applied oscillating signal. The density that

can be obtained using DLCP is also called the drive level density (Ndl), and it is defined as shown below. (Note: In the previous equation the subscripted symbols C1, C2, etc. have the units of capacitance per volt, capacitance per volt squared, etc.)

A capacitance versus frequency (Cf) measurement is helpful to understand the dynamic behavior of PV cells as well. The results of a Cf measurement are often plotted as complex numbers in the impedance plane where this information is known by many names, such as Nyquist plots, Cole-Cole plots, complex impedance plots, etc.

A variety of time domain measurement methods are being developed to evaluate the recombination parameters of solar cells, such as minority carrier lifetime (τ), surface recombination velocity (S) and minority carrier diffusion length (Ld). One of the most popular techniques is open circuit voltage decay (OCVD) where the excitation is supplied either electrically or optically (see figure below). In the electrical case a constant current equal to Isc is forced into the solar cell and the voltage decay across the solar cell is observed after abruptly terminating the current. In the optical case a light pulse is used to stimulate the solar cell instead of a current. For the short circuit condition the current flow across the solar cell is measured after removing the light stimulus, and this is called the short circuit current decay (SCCD).

Each of the various measurement parameters just discussed could be measured with a complex setup of multiple GPETE products and some software to post process the results. A much better way to do it is to use Agilent's B1500A semiconductor device analyzer. The B1500A provides a one box solution with software built-in to make high accuracy and high precision capacitance, time domain, and I-V measurements for PV material testing.

When designing a device with max power point tracking (MPPT) capability such as a solar inverter, micro inverter, or DC optimizer you are going to need to simulate the output of a PV panel or panels to test your MPPT design. This is necessary to verify your design and provide an accurate efficiency spec under a wide variety of weather patterns (I-V curves). Now a lot of engineer new to this type of testing decide to take a standard programmable power supply, connect it remotely to a computer (using GPIB, LAN, USB, etc), and create software with adjustable I-V curve look-up tables with the idea of turning their power supply into a PV panel simulator. This whole concept is shown in the figure (click to enlarge).

You can also find power supply companies out there that sell this exact solution. I am here to save you time, frustration, and money by telling you this method will not work or at least it won't work how you think it will work. With this type PV simulator system the I-V curve 3 dB bandwidth will be < 1 Hz. Most MPPT designs are making load changes and measurements much faster than once per second. Here is a quick breakdown why the bandwidth to this solution is so poor:

The IO latency between the computer and the power supply.

The supply programming time which consists of the time it takes the supply to process a command and the time for the internal analog circuitry to move the output of the supply to where it should be on the curve.

The most limiting factor is that this is a closed loop system, which leads to oscillations in the output. Now to get rid of oscillations digital filtering will need to be added to the software which leads to multiple iterations of back and forth adjustments between the computer and supply to zero in on that point on the I-V curve where the supply output should be.

Because of the overhead just discussed you cannot achieve output bandwidths better than 1 Hz using this solution to simulate the output of a PV panel. For this reason it is not an acceptable test method to verify your MPPT design or spec the efficiency of your MPPT design. Now does this a PV output simulation method have a place in the MPPT hardware test cycle? Because of its relative low cost it could be used in long term reliability testing where you are just interested in continually feeding power through your design over a long period of time to make sure it doesn't break down.

So what is out there to simulate the output of a PV panel? There are two main ways to do it: take a power supply and put some custom analog circuitry around it or purchase a solar array simulator (SAS). I have heard of many different approaches using custom analog circuitry, below is a link to a paper that presents one way to do it:

Of course building a solution yourself comes with a high overhead of simulation, layout, testing, and support. If you want a finished solution you could purchase an SAS. An SAS is not a standard power supply. It is more comparable to a high powered current source with a low output capacitance (< 100 nF) to give it a high output bandwidth. Of course with these more advanced capabilities it comes with a higher price tag than a standard power supply. There is not too many companies out there that make SASs. Agilent is one of the few and below is a link to Agilent's E4360A SAS:

I have noticed that my posts on photovoltaic test are getting lots of hits so here is another one. Here I am going to present a $3k photovoltaic I-V curve measurement system. The measurement system can be seen in the figure below (click on it to enlarge it).

Here is how it works:

The op amp, FET, and Rsense act like a poor mans programmable electronic load with the PV panel connected across it. The op amp will drive the FET (lower its resistance) until the voltage at the op amps negative input equals the voltage at its positive input. If we can control the voltage at the positive input then we can control the current flowing out of the PV panel into the FET and Rsense just like an eload in consant current mode

Setting and stepping the voltage at the positive input of the op amp is done by the 34972A DAQ switch unit. It provides a DAC output from 0 to 15 V. When the DAC is set to 0V the FET is in an open condition and the PV panel is at Voc.

Rsense is 100 mOhm precision shunt. If we set the 34972A's DAC output to .5 V the op amp will drive the FET until the voltage drop across Rsense is .5 V. Since Rsense is 100 mOhm we know that 5 A of current is flowing out of the PV panel through Rsense (Ohm's law: .5 V/.1 Ohm = 5 A).

The 34972A's built-in 61/2 digit DMM combined with plugin MUX switch cards allow us to measure voltage, current, temperature, and more on a large number of channels. In the figure we use one channel to measure the PV panel's voltage, another channel to measure the panel's current (voltage measurement across Rsense), and two other channels to measure temperature.

Putting it all together the way we get the I-V curve is by stepping the DAC's voltage up from 0 V (panel at Voc) until we reach Isc. At each step we measure the panel's output voltage and current to get our I-V curve.

The way we know we have reached Isc is when further voltage steps from the DAC do not result in the voltage across Rsense increasing. At this point the FET is essentially a short.

This photovoltaic I-V curve measurement system will not work well with low voltage low power PV cells since Rsense and the FET cannot actually become a true short. It is better suited for PV modules and panels. Although the hardware is low cost you do need to wrap some type of software around it to control the DAC and gather the measurements (unless you want to do it manually). The value of Rsense and its power handling capability should be chosen based on your PV device's power range and your measurement accuracy needs. Below is a list of parts I used and their approximate cost. This was just a brief overview of the solution if you need more info just comment or email me.

This is a follow-up to my post on 6/11/10 that covered performing MPPT using a DC electronic load (eload). MPPT with an eload is done for design verification and durability testing of Photovoltaic (PV) devices like PV panels and concentrated PV. Besides just performing MPPT related testing, eloads make great solutions for I-V curve characterization for manufacturing and R&D test. They are great for testing high current PV devices like large area cells, modules, panels, and concentrated PV since eloads can sink and measure high current for a low cost. Below is a link to a video on youtube starring yours truly that covers using an eload for characterizing I-V curves.

Eloads are great for outdoor Photovoltaic test but where is the MPPT capability?

Eloads have become a popular solution for outdoor testing of higher power photovoltaic (PV) devices, like PV panels and concentrated PV. The main reason for this is eloads can sink a lot of current at a low cost compared to 2 and 4 quadrant power supplies. The testing is usually of the design verification variety and one of the main roles of the eload is max power point tracking (MPPT) on the output of the PV device. One request of end users of eloads for this application is does the eload have MPPT capability or can you put built-in MPPT capability in the eload? Currently there are no general purpose eloads (that I know of) that have built-in MPPT capabilities. This means it is up to the test engineer to implement an MPPT algorithm in software. This adds time and complexity to the test engineer’s job. Also since the algorithm is in the software it has to deal with IO latency between the computer and the eload which lowers the test systems MPPT speed. To help test engineers out with this challenge I wrote an article entitled “A Photovoltaic MPPT Algorithm for DC Electronic Loads” that was published by Electronic Design and can be found at the link below. The article introduces an ideal algorithm for performing MPPT with an eload. It is ideal because of its low complexity and it keeps IO transactions to a minimum to reduce the affects of IO latency.